scholarly journals Multivariate Hawkes processes: an application to financial data

2011 ◽  
Vol 48 (A) ◽  
pp. 367-378 ◽  
Author(s):  
Paul Embrechts ◽  
Thomas Liniger ◽  
Lu Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Estimation ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Financial Data ◽  
Data Sets ◽  
Hawkes Process ◽  
Science And Engineering ◽  
Hawkes Processes

A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

scholarly journals Multivariate Hawkes processes: an application to financial data

2011 ◽  
Vol 48 (A) ◽  
pp. 367-378 ◽  
Author(s):  
Paul Embrechts ◽  
Thomas Liniger ◽  
Lu Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Estimation ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Financial Data ◽  
Data Sets ◽  
Hawkes Process ◽  
Science And Engineering ◽  
Hawkes Processes

A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Maximum Likelihood Estimation for the Generalized Pareto Distribution and Goodness-of-Fit Test with Censored Data

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Minh H. Pham ◽  
Chris Tsokos ◽  
Bong-Jin Choi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Likelihood Estimation ◽  
R Package ◽  
Goodness Of Fit Test ◽  
Generalized Pareto

The generalized Pareto distribution (GPD) is a flexible parametric model commonly used in financial modeling. Maximum likelihood estimation (MLE) of the GPD was proposed by Grimshaw (1993). Maximum likelihood estimation of the GPD for censored data is developed, and a goodness-of-fit test is constructed to verify an MLE algorithm in R and to support the model-validation step. The algorithms were composed in R. Grimshaw’s algorithm outperforms functions available in the R package ‘gPdtest’. A simulation study showed the MLE method for censored data and the goodness-of-fit test are both reliable.

scholarly journals Zero-Truncated Discrete Two-Parameter Poisson-Lindley Distribution with Applications

2018 ◽  
Vol 22 (2) ◽  
pp. 76-85
Author(s):  
Rama Shanker ◽  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Lindley Distribution ◽  
Coefficients Of Variation ◽  
And Behavior ◽  
Two Parameter

A zero-truncated discrete two-parameter Poisson-Lindley distribution (ZTDTPPLD), which includes zero-truncated Poisson-Lindley distribution (ZTPLD) as a particular case, has been introduced. The proposed distribution has been obtained by compounding size-biased Poisson distribution (SBPD) with a continuous distribution. Its raw moments and central moments have been given. The coefficients of variation, skewness, kurtosis, and index of dispersion have been obtained and their nature and behavior have been studied graphically. Maximum likelihood estimation (MLE) has been discussed for estimating its parameters. The goodness of fit of ZTDTPPLD has been discussed with some data sets and the fit shows satisfactory over zero – truncated Poisson distribution (ZTPD) and ZTPLD. Journal of Institute of Science and TechnologyVolume 22, Issue 2, January 2018, Page: 76-85

scholarly journals On Poisson-Weighted Lindley Distribution and Its Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
R. Shanker ◽  
K. K. Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Mixture ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
And Behavior

In this paper the nature and behavior of its coefficient of variation, skewness, kurtosis and index of dispersion of Poisson- weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution, have been proposed and the nature and behavior have been explained graphically. Maximum likelihood estimation has been discussed to estimate its parameters. Applications of the proposed distribution have been discussed and its goodness of fit has been compared with Poisson distribution (PD), Poisson-Lindley distribution (PLD), negative binomial distribution (NBD) and generalized Poisson-Lindley distribution (GPLD).

scholarly journals Maximum likelihood estimation of the geometric niche preemption model

2021 ◽  
Author(s):  
Jan Graffelman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Ecological Model ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Likelihood Estimator ◽  
Two Samples ◽  
Multinomial Sampling ◽  
Geometric Decay

AbstractThe geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May’s equation. This article proposes a maximum likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.

scholarly journals The ArcTan Lomax Distribution with Properties and Applications

2021 ◽  
pp. 117-125
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Survival Analysis ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
And Mathematics

Here, in this paper, a continuous distribution called ArcTan Lomax distribution with three-parameter has been introduced along with some relevant properties of statistics and mathematics pertaining to the distribution. With the help of three established estimations methods including maximum likelihood estimation (MLE), estimation of the presented distribution’s model parameters is done. Also with the help of a real set of data, the distribution’s goodness-of-fit is examined in contrast to some established models in survival analysis.

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